You can do it in 3 weighings, even with 13 weights, twelve of which are the same. In general, you can do it for (3^n-1)/2 weights in n weighings.
The three is there basically because any weighing has 3 possible outcomes: left higher, even, or right higher; and the 2 is there because the
outlier could be one of 2 things: heavier or lighter.